Bulletin of Mathematical Biology

, 67:1135 | Cite as

Diffusion and home range parameters from rodent population measurements in Panama

  • L. Giuggioli
  • G. Abramson
  • V. M. KenkreEmail author
  • G. Suzán
  • E. Marcé
  • T. L. Yates


Simple random walk considerations are used to interpret rodent population data collected in Hantavirus-related investigations in Panama regarding the short-tailed cane mouse, Zygodontomys brevicauda. The diffusion constant of mice is evaluated to be of the order of (and larger than) 200 meters squared per day. The investigation also shows that the rodent mean square displacement saturates in time, indicating the existence of a spatial scale which could, in principle, be the home range of the rodents. This home range is concluded to be of the order of 70 meters. Theoretical analysis is provided for interpreting animal movement data in terms of an interplay of the home ranges, the diffusion constant, and the size of the grid used to monitor the movement. The study gives impetus to a substantial modification of existing theory of the spread of the Hantavirus epidemic which has been based on simple diffusive motion of the rodents, and additionally emphasizes the importance for developing more accurate techniques for the measurement of rodent movement.


Home Range Mathematical Biology Diffusion Constant Home Range Size Deer Mouse 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Abramson, G., Kenkre, V.M., 2002. Spatio-temporal patterns in the Hantavirus infection. Physical Review E 66, 011912-1-5.Google Scholar
  2. Abramson, G., 2003. Waves of Hanta. In: Kenkre, V.M., Lindenberg, K. (Eds.), Modern Challenges in Statistical Mechanics, Patterns, Noise, and the Interplay of Nonlinearity and Complexity. In: AIP Conference Proceedings, vol. 658. American Institute of Physics, Melville, NY, USA.Google Scholar
  3. Abramson, G., Kenkre, V.M., Yates, T., Parmenter, B., 2003. Traveling waves of infection in the Hantavirus epidemics. Bulletin of Mathematical Biology 65, 519–534.CrossRefGoogle Scholar
  4. Abramson, G., Giuggioli, L., Kenkre, V.M., Dragoo, J.W., Parmenter, R.R., Parmenter, C.A., Yates, T.L., 2004. Diffusion and home range parameters for rodents II. Peromyscus maniculatus in New Mexico. Ecological Complexity (submitted for publication).Google Scholar
  5. Aguirre, M.A., Abramson, G., Bishop, A.R., Kenkre, V.M., 2002. Simulations in the mathematical modeling of the spread of the Hantavirus. Physical Review E 66, 041908-1-5.Google Scholar
  6. Anderson, D.J., 1982. The home range, a new nonparametric estimation technique. Ecology 63(1), 103–112.CrossRefGoogle Scholar
  7. Ballard, M., Kenkre, V.M., Kuperman, M.N., 2004. Periodically varying externally imposed environmental effects on population dynamics. Physical Review E 70, 031912-1-7.Google Scholar
  8. Botten, J., Mirowsky, K., Ye, C., Gottlieb, K., Saavedra, M., Ponce, L., Hjelle, B., 2002. Shedding and intracage transmission of Sin Nombre hantavirus in the deer mouse (Peromyscus maniculatus) model. Journal of Virology 76(15), 7587–7594.CrossRefGoogle Scholar
  9. Buceta, J., Escudero, C., de la Rubia, F.J., Lindenberg, K., 2004. Outbreaks of Hantavirus induced by seasonality. Physical Review E 69, 021906-1-8.Google Scholar
  10. Burt, W.H., 1943. Territoriality and home range concepts as applied to mammals. Journal of Mammalogy 24, 346–352.Google Scholar
  11. Childs, J.E., Ksiazek, T.G., Spiropoulou, C.F., Krebs, J.W., Morzunov, S., Maupin, G.O., Gage, K.L., Rollin, P.E., Sarisky, J., Enscore, R.E., Frey, J.K., Peters, C.J., Nichol, S.T., 1994. Serologic and genetic identification of Peromyscus maniculatus as the primary rodent reservoir for a new hantavirus in the southwestern United States. Journal of Infectious Diseases 169, 1271–1280.Google Scholar
  12. Ford, R.G., 1979. The analysis of space use patterns. Journal of Theoretical Biology 76, 125–155.CrossRefGoogle Scholar
  13. Kenkre, V.M., 2003. Memory formalism, nonlinear techniques, and kinetic equation approaches. In: Kenkre, V.M., Lindenberg, K. (Eds.), Modern Challenges in Statistical Mechanics, Patterns, Noise, and the interplay of Nonlinearity and Complexity. In: AIP Conference Proceedings, vol. 658. American Institute of Physics, Melville, NY, USA.Google Scholar
  14. Kenkre, V.M., 2004. Results from variants of the Fisher equation in the study of epidemics and bacteria. Physica A 342, 242–248.CrossRefGoogle Scholar
  15. Kenkre, V.M., Abramson, G., Giuggioli, L., Neto, G.C., 2004. Generalized models for the spread of Hantavirus. University of New Mexico preprint.Google Scholar
  16. Kuperman, M.N., Kenkre, V.M., 2004. Spatial features of population dynamics, effects of mutual interactions and of interaction with the environment (unpublished).Google Scholar
  17. Mills, J.N., Ksiazek, T.G., Peters, C.J., Childs, J.E., 1999. Long-term studies of hantavirus reservoir populations in the southwestern United States, a synthesis. Emerging Infectious Diseases 5(1), 135–142.Google Scholar
  18. Murray, J.D., 1993. Mathematical Biology, 2nd edition. Springer, New York, USA.zbMATHGoogle Scholar
  19. Nichol, S.T., Spiropoulou, C.F., Morzunov, S., Rollin, P.E., Ksiazek, T.G., Feldmann, H., Sanchez, A., Childs, J., Zaki, S., Peters, C.J., 1993. Genetic identification of a hantavirus associated with an outbreak of acute respiratory illness. Science 262, 914–917.Google Scholar
  20. Ovaskainen, O., 2004. Habitat-specific movement parameters estimated using mark-recapture data and a diffusion model. Ecology 85, 242–257.Google Scholar
  21. Parmenter, C.A., Yates, T., Parmenter, R.R., Mills, J.N., Childs, J.E., Campbell, M.L., Dunnum, J.L., Milner, J., 1998. Small mammal survival and trapability in mark-recapture monitoring programs for hantavirus. Journal of Wildlife Diseases 34(1), 1–12.Google Scholar
  22. Parmenter, C.A., Yates, T.L., Parmenter, R.R., Dunnum, J.L., 1999. Statistical sensitivity for detection of spatial and temporal patterns in rodent population densities. Emerging Infectious Diseases 5, 118–125.CrossRefGoogle Scholar
  23. Parmenter, R.R., Yates, T.L., Anderson, D.R., Burnham, K.P., Dunnum, J.L., Franklin, A.B., Friggens, M.T., Lubow, B.C., Miller, M., Olson, G.S., Parmenter, C.A., Pollard, J., Rextad, E., Shenk, T.M., Stanley, T.R., White, G.C., 2003. Small-mammal density estimation, a field comparison of grid-based vs. web-based density estimators. Ecological Monographs 73(1), 1–26.Google Scholar
  24. Schmaljohn, C., Hjelle, B., 1997. Hantaviruses, a global disease problem. Emerging Infectious Diseases 3(2), 95–104.CrossRefGoogle Scholar
  25. Suzán, G., Marcé, E., Parmenter, R.R., Giermakowski, J.T., Mills, J., Armien, B., Armien, A., Pascale, J.M., Zaldivar, Y., Salazar, J., Yates, T.L., 2004. Responses of hantavirus host communities in Panama to species removal. Presented at the 84th Annual Meeting of the American Society of Mammalogists. 12–16 June 2004. Humboldt State University, Arcata, California, USA.Google Scholar
  26. Vincent, M.J., Quiroz, E., Gracia, F., Sánchez, A.J., Ksiazek, T.G., Kitsutani, P.T., Ruedas, L.A., Tinnin, D.S., Cáceres, L., García, A., Rollin, P., Mills, J., Peters, C.J., Nichol, S.T., 2000. Hantavirus pulmonary syndrome in Panama, identification of novel hantaviruses and their likely reservoirs. Virology 277, 14–19.CrossRefGoogle Scholar
  27. Yates, T.L., Mills, J.N., Parmenter, C.A., Ksiazek, T.G., Parmenter, R.R., Vande Castle, J.R., Calisher, C.H., Nichol, S.T., Abbott, K.D., Young, J.C., Morrison, M.L., Beaty, B.J., Dunnum, J.L., Baker, R.J., Salazar-Bravo, J., Peters, C.J., 2002. The ecology and evolutionary history of an emergent disease, Hantavirus Pulmonary Syndrome. Bioscience 52, 989–998.Google Scholar

Copyright information

© Society for Mathematical Biology 2005

Authors and Affiliations

  • L. Giuggioli
    • 1
  • G. Abramson
    • 1
    • 2
  • V. M. Kenkre
    • 1
    Email author
  • G. Suzán
    • 3
  • E. Marcé
    • 3
  • T. L. Yates
    • 3
  1. 1.Consortium of the Americas for Interdisciplinary ScienceUniversity of New MexicoAlbuquerqueUSA
  2. 2.Centro Atómico BarilocheCONICET and Instituto BalseiroSan Carlos de Bariloche, Río NegroArgentina
  3. 3.Department of BiologyUniversity of New MexicoAlbuquerqueUSA

Personalised recommendations